Question

IF cos A =2 sin A, find the value of cosec A .

• A. 1
• B. $\pm \sqrt{5}$
• C. $\frac{1}{2}$
• D. $\pm \sqrt{3}$

Answer 1

Answer: (B)

$\pm \sqrt{5}$

Given $\cos A=2\sin A$
OR ${\cos }^{2}A=5{\sin }^{2}A$
or $1-{\sin }^{2}A=4{\sin }^{2}A$
OR $5{\sin }^{2}A=1$
or $\sin A=\pm \frac{1}{\sqrt{5}}$
$\therefore cosecA=\pm \sqrt{5}$